Using Euler's identity, find real positive constants $\displaystyle c$ and $\displaystyle \phi$ for all real $\displaystyle t$ such that:

$\displaystyle 3 \cos (2t) - 4 \sin (2t + \frac{\pi}{4}) = c \cos (2t + \phi)$

I tried substituting the Euler formula for all sine and cosine values to get:

$\displaystyle \frac{3}{2}(e^{j2t}+e^{-j2t}) - \frac{4}{2}(e^{j2t}e^{j\pi /4}-e^{-j2t}e^{-j\pi /4}) = \frac{c}{2}(e^{j2t}e^{j\phi}+e^{-j2t}e^{-j\phi})$

Which suggests:

$\displaystyle ce^{j\phi} = 3 - 4 e^{j\pi /4}$

Which I don't see a solution to. Any ideas?